On 7/28/2012 9:35 AM, Bruno Marchal wrote:

    This is a "degeneracy" problem, everything looks, acts and even is
    one and the same thing, so how is there any differentiation that
    allows a plurality to obtain?

0 ≠ s(0) ≠ s(s(0)) ≠ ....

I need to explain myself on this claim for the sake of others that might be confused and yet open to understanding.

The non-equivalence that Bruno points out here with "0 ≠ s(0) ≠ s(s(0)) ≠ .... " is correct, but that correctness changes when we introduce Godel Numbering. Godel numbering is the coding of statements about numbers as numbers and so has the effect of making the " ≠ " ambiguous and thus making the non-equivalence of numbers degenerate. Once we introduce the idea that numbers can code for other numbers then it follows that numbers are no longer uniquely different from each other. Therefore the plurality of numbers with regard to their ability to define multiple unique quantities vanishes.



"Nature, to be commanded, must be obeyed."
~ Francis Bacon

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